This invention pertains generally to arrays of components, such as an array of deflectors as used in a charged-particle-beam (CPB) optical system, that function cooperatively to achieve a desired performance of the system comprising the components. The invention also pertains to methods for exploring a xe2x80x9cdesign spacexe2x80x9d to find an optimal combination of respective values of configurational and/or operational parameters of the components to achieve the desired performance. Such methods are especially useful in CPB microlithography systems that comprise one or more arrays of multiple deflectors. The deflectors must function cooperatively with each other to produce a desired imaging quality. For example, individual respective values of configurational and/or operational parameters for each deflector must be optimized in view of the parameters of the other deflectors to produce a combination of values of the parameters achieving the desired imaging quality.
In view of the resolution limits of optical microlithography (microlithography performed using a light beam such as a beam of ultraviolet light), charged-particle-beam (CPB) microlithography has received considerable attention as a possible successor technology. The reasons are similar to the argument that electron microscopy achieves greater resolution than optical microscopy.
Examples of conventional CPB microlithography include (a) spot-beam exposure systems, (b) variable-shaped-beam exposure systems, and (c) block exposure systems. Each of these exposure systems offer prospects of much greater resolution than so-called xe2x80x9cone-shotxe2x80x9d optical microlithography systems, but are grossly inferior in terms of throughput. Specifically, in exposure systems (a) and (b), throughput is low because exposure is accomplished by tracing the pattern using a beam having an extremely small round or square spot diameter, respectively. It is immediately apparent that a complex pattern requires a large amount of time to xe2x80x9cdrawxe2x80x9d line-by-line. Exposure system (c) was developed to achieve improved throughput over systems (a) and (b). In exposure system (c), throughput is improved because the pattern includes an array containing a large number (typically thousands) of individual repeat units, such as the memory cells on a memory chip. The repeat unit normally is very small, typically about 5 xcexcm square on the substrate. The repeat unit is defined on a reticle and is exposed over and over again within a region on the substrate corresponding to the chip. As readily understood, considerable time is required to expose the array in each chip, which results in low throughput. Also, this technique is not used to transfer non-repeated portions of the chip pattern. Instead, the non-repeated portions usually are exposed by direct writing using a variable-shaped beam. This need to exploit multiple different techniques to expose each chip further compromises throughput. As a result, system (c) does not provide the throughput required for mass-production wafer fabrication.
A technique offering prospects of substantially greater throughput than the techniques summarized above involves exposing, in a single xe2x80x9cshot,xe2x80x9d a reticle defining the entire pattern to be transferred to a chip or defining a pattern for multiple chips. The reticle is exposed with xe2x80x9cdemagnification,xe2x80x9d by which is meant that the reticle image is smaller (usually by an integer factor termed a xe2x80x9cdemagnification factorxe2x80x9d) than the corresponding pattern as defined on the reticle. Whereas the throughput potentially achievable using this technique is at least as good as currently achievable using optical microlithography, this technique unfortunately has several serious problems. One problem is the current impossibility of fabricating a reticle configured to be exposed in a single shot of a charged particle beam. Another problem is the current impossibility of adequately correcting off-axis aberrations, especially in peripheral regions of the large image produced by the charged particle beam.
A more recently considered approach is termed xe2x80x9cdivided-reticlexe2x80x9d pattern transfer, which involves dividing the pattern, as defined on the reticle, into multiple individual exposure units usually termed xe2x80x9csubfields.xe2x80x9d Each subfield is exposed individually onto a respective region on the wafer. The subfield images are transferred to the wafer so that, after exposing all the subfields, the subfield images are xe2x80x9cstitchedxe2x80x9d together in a contiguous manner to form the entire chip pattern. Divided-reticle pattern transfer allows exposures to be made over an optically wide field with much better resolution and accuracy than could be obtained by exposing the entire reticle in one shot. Although divided-reticle pattern transfer does not yet achieve the same throughput as optical microlithography, the throughput nevertheless is much better than obtainable using the other CPB microlithography techniques summarized above.
Certain aspects of divided-reticle pattern transfer are shown in FIGS. 5 and 6. FIG. 5 depicts a wafer on which multiple chips have been exposed. As exposed, each chip comprises multiple xe2x80x9cstripes,xe2x80x9d and each stripe comprises multiple subfields arranged in rows. This same divided arrangement of stripes and subfields is used to define the pattern on the reticle. FIG. 6 depicts an actual exposure. For exposure, the reticle and wafer are mounted on respective stages (not shown but well understood in the art) configured to move the reticle and wafer horizontally (in the figure) as required for exposure. During exposure of a stripe (a portion of which is shown), the reticle stage and wafer stage both move along the longitudinal line of the respective stripes. Movements of the reticle and wafer are at constant respective velocities (but in opposite directions) in accordance with the demagnification ratio. Meanwhile, the charged particle beam incident on the reticle (the beam incident on the reticle is termed the xe2x80x9cillumination beamxe2x80x9d and passes through an xe2x80x9cillumination-optical systemxe2x80x9d to the reticle) illuminates the subfields on the reticle row-by-row and subfield-by-subfield within each row (the rows extend perpendicularly to the movement directions of the reticle and wafer). As each subfield is illuminated in this manner, the portion of the illumination beam passing through the respective subfield (now termed the xe2x80x9cpatterned beamxe2x80x9d or xe2x80x9cimaging beamxe2x80x9d) passes through a projection-optical system to the wafer.
During exposure of a stripe, to expose the rows and subfields within each row of the stripe in a sequential manner, the illumination beam is deflected at right angles to the movement direction of the reticle stage and the patterned beam is deflected at right angles to the movement direction of the wafer stage. After completing exposure of each row, the illumination beam is deflected in the opposite direction, as shown in FIG. 6, to expose the subfields in the next row of the stripe. This exposure technique reduces extraneous deflections of the beam and improves throughput.
Normally, on the reticle, each subfield is surrounded by xe2x80x9cstrutsxe2x80x9d configured as a lattice separating the subfields from one another and providing the reticle with considerable rigidity and mechanical strength. The struts also ensure that, in each shot, only the respective subfield is illuminated and exposed onto the wafer.
In a divided-reticle CPB projection-microlithography apparatus, throughput is improved by performing exposures using a relatively high beam current in the illumination-optical system and projection-optical system. To perform exposures with a high beam current, it usually is necessary to enlarge the area of the reticle being exposed per shot, and to accelerate the beam with a high beam-acceleration voltage, so as to reduce image blur due to the Coulomb effect.
Throughput also can be increased by performing exposures at the widest practical range of beam deflection. Enlarging the deflection field in this manner results in a corresponding increase in the width of the stripes, which decreases the amount of time that must be dedicated to mechanically shifting positions of the wafer and reticle. Enlarging the deflection field also reduces the number of times that scanning of the beam must reverse direction (FIG. 6). As a result, the time overhead consumed in starting and stopping motions of the stages and the beam is reduced throughput correspondingly increased. Unfortunately, imparting wider deflections of the beam results in the beam passing through areas of the reticle that are far off the axis of the illumination-optical and projection-optical systems, causing substantial deflection aberrations. To reduce these aberrations substantially, deflectors are provided in the illumination-optical and projection-optical systems. The deflectors are energized individually in a controlled manner to deflect the beam as required to correct the particular aberrations for each subfield.
In view of the number of deflectors required and the need to energize each deflector in a different manner from one another in each subfield and from one subfield to the next, it is difficult to obtain an optimum combination of deflector-energization parameters for each subfield. Software programs currently are available for determining parameters and achieving a certain level of deflector control. However, the current algorithms developed for that software exhibit only a limited extent and quality of performance, resulting in a falling apart of local solutions and the existence of situations in which proper solutions are not obtainable. Furthermore, current software for deflector control requires extensive experience and training to set up and use.
In view of the shortcomings of conventional methods and apparatus as summarized above, an object of the invention is to provide methods for configuring and/or operating multiple components that must function cooperatively to achieve a desired performance result. For example, the methods can be applied to configuring and/or operating an array of multiple deflectors in a charged-particle-beam (CPB) optical system or a CPB projection-microlithography apparatus including such an optical system, so as to produce, for each subfield to be exposed, an optimal combination of exposure parameters, while avoiding the convergence to a local solution rather than an optimal solution.
To such ends, and according to a first aspect of the invention, methods are provided in the context of a CPB optical system comprising multiple components each having at least one parameter the value of which is established so as to cause, when all such components of the CPB optical system are configured or operated in a coordinated manner according to the respective values of the parameters, the CPB optical system to operate in a manner producing a desired performance result. The methods allow determinations of respective values of the parameters for the components. According to an embodiment of such a method, and according to the analysis model employed in the method, each respective value of a respective parameter is regarded as a respective xe2x80x9cgene.xe2x80x9d Each respective combination of values of the parameters is regarded as a respective xe2x80x9cchromosomexe2x80x9d and each respective configuration of the CPB optical system according to the respective chromosome is regarded as a respective xe2x80x9cspecies.xe2x80x9d To begin execution of the method, each parameter has a respective initial condition gene, wherein each of NA species in a group xe2x80x9cAxe2x80x9d comprises a respective chromosome of the initial condition genes. An evaluation function is defined, wherein values of the evaluation function are related to respective qualities of a performance characteristic of the CPB optical system. A threshold value is established for the evaluation function. From the group-A species, a group xe2x80x9cBxe2x80x9d including NB species (wherein NBxe2x89xa6NA) is selected in which each constituent species has a high respective value of the evaluation function. From the group-B species, groups xe2x80x9cCNDxe2x80x9d (in which each group includes NC individuals) are selected to produce a group xe2x80x9cDxe2x80x9d including ND species. Each species in group D comprises a respective chromosome produced by recombination of one or more genes from respective chromosomes of species in the groups CND. The group D of ND species is produced from the NC individuals. From the group D, a new group B including NB species is selected. The steps of selecting the group B through producing a species of group D are repeated a predetermined number of times or until a species is produced in group D having a respective value of the evaluation function that exceeds the threshold. Finally, the species produced in the previous step is employed to define the respective combination of values of the parameters for configuring the components or for operating the components in the coordinated manner.
A xe2x80x9cspeciesxe2x80x9d as the term is used above is a distinctive combination of respective values for the subject parameters for all the subject components. Each respective value of a subject parameter is termed a xe2x80x9cgene.xe2x80x9d For example, if the subject components are six deflectors as arrayed in a CPB optical system, and each deflector has associated therewith respective values of two different parameters, then each species is represented by a distinctive combination of 12 genes. For any species, the array of genes can be represented as a xe2x80x9cchromosomexe2x80x9d containing the gene sequence of the particular species. Hence, species having identical gene sequences are identical species, and species in which even one gene is different are different species from one another.
An xe2x80x9cindividualxe2x80x9d as used herein is a unit having a gene sequence that is the same as the gene sequence of its affiliated species.
In this embodiment of the subject methods, a genetic algorithm is employed to find, for the array of components, an optimal species, i.e., an optimal combination of configurational and/or operational parameters, thereby providing an optimal performance of the system. An evaluation function is employed. From among a certain number of species, the species that are selected have higher respective values of the evaluation function than species that are not selected. From the group of selected species, individuals are selected to be xe2x80x9cparents,xe2x80x9d according to a specified rule (e.g., selection criterion or probability). Among the parents, multiple xe2x80x9cmatingsxe2x80x9d are performed. In each xe2x80x9cmating,xe2x80x9d multiple parents produce a xe2x80x9cchildxe2x80x9d species of which the chromosome typically contains respective genes from each of the parents. In other words, in each mating, the genes from the parents are xe2x80x9ccrossedxe2x80x9d or xe2x80x9crecombinedxe2x80x9d to produce a new combination of genes in the child. Among the xe2x80x9cchildren,xe2x80x9d species are selected having xe2x80x9chigherxe2x80x9d respective values of the evaluation function than species that are not selected. Among the selected children species, individuals are selected according to a specified rule to serve as a second generation of parents. Children (xe2x80x9cgrandchildrenxe2x80x9d) with crossed genes are produced from respective matings of this second generation of parents. This process of selecting parents and performing matings is repeated as required to produce a progeny species having an optimal value of the evaluation function.
In the xe2x80x9cmatings,xe2x80x9d as noted above, parental genes are xe2x80x9ccrossed,xe2x80x9d resulting in some or all the parental genes being mixed (recombined) in the resulting child. Hence, it is possible to evaluate a wide range of species and avoid convergence on a local solution (rather than an optimal solution). Also, since species having higher respective values of the evaluation function are carried forward as candidate parents to be mated to produce the subsequent generation, there is a high probability that the children resulting from that mating will have even higher respective values of the evaluation function, thereby facilitating the finding of an optimal solution.
The phrase xe2x80x9cmixing or exchanging at least some of the genes from chromosomesxe2x80x9d in any of the stated groups indicates that one or both mixing and exchanging (generally termed xe2x80x9crecombinationxe2x80x9d) can be performed. This phrase also includes situations in which one is performed in a first subset of chromosomes, the other is performed in a second subset of chromosomes, and both are performed in a third subset of chromosomes.
Instances may arise in which several species in the D group unintentionally have the same chromosomes. In such instances, the same-chromosome species nevertheless are regarded as different species.
By way of example, recombination of genes occurs between a xe2x80x9cmalexe2x80x9d parent and a xe2x80x9cfemalexe2x80x9d parent (these terms are used for convenience in this specification). Since, in the subject methods, there is no actual distinction between male and female, it will be understood that gene mixing and/or exchange (recombination) can occur between two individuals. Alternatively, gene recombination also can occur between three or more individuals. To illustrate, an exchange of genes between three individuals a, b, c can be performed in sequence, wherein some of a""s genes are moved into b""s chromosome, some of b""s genes are moved into c""s chromosome, and some of c""s genes are moved into a""s chromosome. Recombination of genes between three or more individuals typically consists of substituting the various genes for corresponding genes in the three or more individuals, according to a calculation formula serving as an independent variable.
Species having higher respective values of the evaluation function are carried forward. Alternatively, the evaluation function can be formulated such that species having xe2x80x9clowerxe2x80x9d respective values thereof desirably are selected to be carried forward. Such an alternative situation is self-evident, and both situations are clearly equivalent and encompassed by the invention.
In this embodiment of the method, in the various steps that are repeated, the respective numbers of species NB, NC in the B and CND groups can be changed in each repeat.
In the description below, the term xe2x80x9creticlexe2x80x9d is used. However, xe2x80x9creticlexe2x80x9d often is used interchangeably with xe2x80x9cmask,xe2x80x9d and these terms are synonymous herein.
Furthermore, in the descriptions herein, the subject components (e.g., of a CPB optical system) are not construed necessarily to indicate all of the components, but rather typically refer to those components for which optimum parameters are to be determined. In addition, among the components of a system such as CPB optical system, the components for which optimum parameters are to be determined can be subdivided into several groups, wherein methods as described herein are used to determine respective optimum parameters for one or more of the groups of components. In such an instance, if no interference exists between the respective parameters of one group and the respective parameters of another group, then the number of combinations can be minimized and optimization can be simplified by determining the optimum parameters for respective components of the various groups as a whole. Viewed from a different perspective, the concept of evaluating separate groups of respective components corresponds with analyzing the genes of multiple chromosomes, wherein each chromosome corresponds to a respective group of components and the genes of each chromosome correspond to the components in the respective group.
In the step of selecting the group-CND individuals from the group-B species, the groups CND are selected in a manner such that species having high respective values of the evaluation function have a high probability of being selected. Hence, the probability is increased that species having high respective values of the evaluation function will be crossed with each other, thereby increasing the probability that subsequent generations will include species having even higher respective values. The respective probability can be expressed as a ratio of the respective value of the evaluation function to a sum of respective values of the evaluation function among the group B of species. Thus, it is easier to select species, having high respective values of the evaluation function, as high-priority parents.
The method can include the step of substituting a specified number NE (wherein NE less than ND) of species, having low respective values of the evaluation function, in the group D with the specified number NE of species, having high respective values of the evaluation function, in the group B. When new genes are obtained by recombining genes from parents, it is possible that a child will have a lower respective value of the evaluation function than any of its parents. This is xe2x80x9cdegradation,xe2x80x9d which can be prevented by unconditionally carrying forward a predetermined number of parents in order, starting with the parent having the highest respective value of the evaluation function. If a specified number of parents are carried forward in this manner, then the number of children selected decreases by a corresponding amount.
The method can include the step of forming a group (D+F) of species by adding a specified number NF of species, having high respective values of the evaluation function, in the group B to the species in group D, wherein the (D+F) group is substituted for the group A. The basic concept of this scheme is the same as described in the previous paragraph. However, rather than decreasing the number of children species by the added number of parent species, a combination of the two is utilized as the new parent species. The effect is the same as described in the previous paragraph.
In the step of selecting the groups CND of individuals to produce a group D of species, the genes can be recombined according to a weighted average of respective values, of the evaluation function, of the genes. In this scheme, since the genes of individuals destined to be parents will become the genes of the respective child by weighting the genes by their respective values of the evaluation function and rendering a weighted average, the effects of the genes (parameters) having the higher respective values of the evaluation function can be carried forward substantially, thereby increasing the probability of creating species having high respective values of the evaluation function.
The step of selecting the groups CND of individuals to produce a group D of species can include changing the genes in the respective chromosomes of at least some of the species in group D by respective specified values, respective specified values randomly selected from a group of values within a specified range, or to respective values randomly selected from a group of values within a specified range. This variation allows for the testing of xe2x80x9cmutations,xe2x80x9d wherein species having respective chromosomes with greatly different characteristics are produced by changing (xe2x80x9cmutatingxe2x80x9d) some or all of the genes of a species. The genes can be mutated by a specified value, by a value randomly selected from a group of values within a specified range, or to a value randomly selected from a group of values within a specified range. Thus, the search space is broadened and the probability of convergence to a local solution (rather than to an optimal solution) is minimized. However, randomly selected values desirably are limited to ranges considered in the design of the subject system to prevent combinations of parameters that are useless in the subject system.
The number of species that will be mutated can be reduced, before the mutation and after the recombination of genes, by excluding species having high respective values of the evaluation function. If, in the scheme summarized in the preceding paragraph, species having high respective values of the evaluation function are obtained before making mutations, these xe2x80x9chigh-valuexe2x80x9d species can be excluded from the mutation. Also, the xe2x80x9cmutationxe2x80x9d is selected from the remaining xe2x80x9clow-valuexe2x80x9d species. After new chromosomes are created by recombining some or all of the parental genes or by changing some of the parental genes, the respective values of the evaluation function of the newly created species are found. This exclusion prevents changing the xe2x80x9chigh-valuexe2x80x9d species to xe2x80x9clow-valuexe2x80x9d species by the mutation.
After the xe2x80x9crepeat-stepsxe2x80x9d step of the method summarized above, a second evaluation function can be defined. Values of the second evaluation function can be related to respective qualities of a performance characteristic of the system. A threshold value for the second evaluation function is established. Then, the noted xe2x80x9crepeat-stepsxe2x80x9d step is performed a predetermined number of times or until a species is produced in the group D having a respective value of the second evaluation function that exceeds the threshold for the second evaluation function. Whenever there are multiple target values in a system design, evaluation criteria can be set using different functions. As a result, individual target values need not be within requisite ranges even through the specified value of an evaluation function is obtained. In this scheme, multiple evaluation functions are employed, and a combination of xe2x80x9chigh-valuexe2x80x9d species is found by first repeatedly performing the noted steps using one of the evaluation functions. The resulting children then are used in repeatedly performed steps in which the other evaluation function is employed. The species derived at the end of all iterations is employed in the system. It is highly likely that this ultimate species meets all numerical parametric requirements.
The method can include the step of executing a hill-climbing technique on the determined respective values of at least some of the parameters to obtain a combination of respective values of the parameters having an optimal respective value of the evaluation function. In the methods and variations of the methods summarized above, a key characteristic is the introduction of randomness that serves to broaden the search space and to prevent the convergence to a local solution rather than to an optimal solution. However, basing a method on randomness can result in slow convergence, thereby increasing the probability that an optimal solution will not be found. Hence, searching can be performed until a nearly optimal solution is found, while avoiding convergence to a local solution rather than to an optimal solution. Afterward, the search can be continued by the xe2x80x9chill-climbingxe2x80x9d method as described herein.
According to another aspect of the invention, CPB optical systems are provided that comprise multiple components of which respective parameters have respective values configured according to any of the methods summarized above. Since the parameters for the components constituting the CPB optical system thus are configured and/or operated optimum values of relevant parameters, distortion and blur are reduced, allowing patterns with ultra-fine linewidths to be exposed and transferred accurately.
According to another aspect of the invention, exemplary CPB optical systems are provided, exhibiting a number of favorable parametric qualities. For example, in an exemplary system, the angle of incidence of the beam to the reticle is xe2x89xa60.125 mrad, blur is xe2x89xa61 xcexcm, and distortion in the subfields is xe2x89xa65 xcexcm. These parameters are all met under certain stated conditions and where the exit angle of the beam from the beam-shaping aperture of the system is xe2x89xa61 mrad.